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Abstract We explore possible advantages of cyclic spectroscopy for observations of pulsars in instances where full cyclic deconvolution is not possible. We compute cyclic merits and full-deconvolution regime boundaries for pulsars observed by NANOGrav and discuss which sources stand to benefit the most from using cyclic spectroscopy when observed with the Green Bank Telescope and DSA-2000 in a given frequency range. We compare data products, namely the wavefield, in both full-deconvolution and partial-deconvolution regimes to demonstrate what can be accomplished with incomplete phase retrieval. Additionally, we show how some phase retrieval can still be achieved in the partial-deconvolution regime and how this allows for additional information in scintillation-based data products, like the dynamic wavefield power, compared to what can be found in traditional dynamic spectra. An examination of dynamic wavefield phase as a function of observing frequency reveals more complete phase retrieval is achieved the closer one gets to the full-deconvolution regime, agreeing with the expectations of cyclic merit. While we demonstrate that fragmentary recovery of the secondary wavefield can be accomplished in the partial-deconvolution regime, we advocate for a synergistic approach with phase retrieval methods like theθ−θtransform, although we also provide discussion about shortcomings of this strategy. Finally, we use the combination of modest cyclic merit and lack of discernible results for PSR J1903+0327 to motivate the creation of an updated “cyclic merit 2.0,” which relies on scintillation bandwidth instead of observing bandwidth. 

Abstract A pulsar’s scintillation bandwidth is inversely proportional to the scattering delay, making accurate measurements of scintillation bandwidth critical to characterize unmitigated delays in efforts to measure low-frequency gravitational waves with pulsar timing arrays. In this pilot work, we searched for a subset of known pulsars within ∼97% of the data taken with the Puerto Rico Ultimate Pulsar Processing Instrument for the AO327 survey with the Arecibo telescope, attempting to measure the scintillation bandwidths in the data set by fitting to the 2D autocorrelation function of their dynamic spectra. We successfully measured 38 bandwidths from 23 pulsars (six without prior literature values), finding that: almost all of the measurements are larger than the predictions from NE2001 and YMW16 (two popular galactic models); NE2001 is more consistent with our measurements than YMW16; Gaussian fits to the bandwidth are more consistent with both electron density models than Lorentzian ones; and for the 17 pulsars with prior literature values, the measurements between various sources often vary by a few factors. The success of Gaussian fits may be due to the use of Gaussian fits to train models in previous work. The variance of literature values over time could relate to the scaling factor used to compare measurements, but also seems consistent with time-varying interstellar medium parameters. This work can be extended to the rest of AO327 to further investigate these trends, highlighting the continuing importance of large archival data sets for projects beyond their initial conception. 

Abstract We use the upgraded Giant Metrewave Radio Telescope (uGMRT) to measure scintillation arc properties in six bright canonical pulsars with simultaneous dual-frequency coverage. These observations, at frequencies from 300 to 750 MHz, allowed for detailed analysis of arc evolution across frequency and epoch. We perform more robust determinations of frequency dependence for arc curvature, scintillation bandwidth, and scintillation timescale, and comparison between arc curvature and pseudo-curvature than allowed by single-frequency-band-per-epoch measurements, which we find to agree with theory and previous literature. We find a strong correlation between arc asymmetry and arc curvature, which we have replicated using simulations, and attribute to a bias in the Hough transform approach to scintillation arc analysis. Possible evidence for an approximately week-long timescale over which a given scattering screen dominates signal propagation was found by tracking visible scintillation arcs in each epoch in PSR J1136+1551. The inclusion of a 155-minute observation allowed us to resolve the scale of scintillation variations on short timescales, which we find to be directly tied to the amount of interstellar medium sampled over the observation. Some of our pulsars showed either consistent or emerging asymmetries in arc curvature, indicating instances of refraction across their lines of sight. Significant features in various pulsars, such as multiple scintillation arcs in PSR J1136+1551 and flat arclets in PSR J1509+5531, that have been found in previous works, were also detected. The simultaneous multiple-band observing capability of the upgraded GMRT shows excellent promise for future pulsar scintillation work. 

Abstract We simulate scattering delays from the interstellar medium to examine the effectiveness of three estimators in recovering these delays in pulsar timing data. Two of these estimators use the more traditional process of fitting autocorrelation functions to pulsar dynamic spectra to extract scintillation bandwidths, while the third estimator uses the newer technique of cyclic spectroscopy on baseband pulsar data to recover the interstellar medium’s impulse response function. We find that either fitting a Lorentzian or Gaussian distribution to an autocorrelation function or recovering the impulse response function from the cyclic spectrum are, on average, accurate in recovering scattering delays, although autocorrelation function estimators have a large variance, even at high signal-to-noise ratio (S/N). We find that, given sufficient S/N, cyclic spectroscopy is more accurate than both Gaussian and Lorentzian fitting for recovering scattering delays at specific epochs, suggesting that cyclic spectroscopy is a superior method for scattering estimation in high-quality data. 

Abstract Pulsar timing array observations have found evidence for an isotropic gravitational-wave background with the Hellings–Downs angular correlations between pulsar pairs. This interpretation hinges on the measured shape of the angular correlations, which is predominantly quadrupolar under general relativity. Here we explore a more flexible parameterization: we expand the angular correlations into a sum of Legendre polynomials and use a Bayesian analysis to constrain their coefficients with the 15 yr pulsar timing data set collected by the North American Nanohertz Observatory for Gravitational Waves (NANOGrav). When including Legendre polynomials with multipolesℓ≥ 2, we only find a significant signal in the quadrupole with an amplitude consistent with general relativity and nonzero at the ∼95% confidence level and a Bayes factor of 200. When we include multipolesℓ≤ 1, the Bayes factor evidence for quadrupole correlations decreases by more than an order of magnitude due to evidence for a monopolar signal at approximately 4 nHz, which has also been noted in previous analyses of the NANOGrav 15 yr data. Further work needs to be done in order to better characterize the properties of this monopolar signal and its effect on the evidence for quadrupolar angular correlations. 

Abstract Evidence has emerged for a stochastic signal correlated among 67 pulsars within the 15 yr pulsar-timing data set compiled by the NANOGrav collaboration. Similar signals have been found in data from the European, Indian, Parkes, and Chinese pulsar timing arrays. This signal has been interpreted as indicative of the presence of a nanohertz stochastic gravitational-wave background (GWB). To explore the internal consistency of this result, we investigate how the recovered signal strength changes as we remove the pulsars one by one from the data set. We calculate the signal strength using the (noise-marginalized) optimal statistic, a frequentist metric designed to measure the correlated excess power in the residuals of the arrival times of the radio pulses. We identify several features emerging from this analysis that were initially unexpected. The significance of these features, however, can only be assessed by comparing the real data to synthetic data sets. After conducting identical analyses on simulated data sets, we do not find anything inconsistent with the presence of a stochastic GWB in the NANOGrav 15 yr data. The methodologies developed here can offer additional tools for application to future, more sensitive data sets. While this analysis provides an internal consistency check of the NANOGrav results, it does not eliminate the necessity for additional investigations that could identify potential systematics or uncover unmodeled physical phenomena in the data. 

Abstract Recently we found compelling evidence for a gravitational-wave background with Hellings and Downs (HD) correlations in our 15 yr data set. These correlations describe gravitational waves as predicted by general relativity, which has two transverse polarization modes. However, more general metric theories of gravity can have additional polarization modes, which produce different interpulsar correlations. In this work, we search the NANOGrav 15 yr data set for evidence of a gravitational-wave background with quadrupolar HD and scalar-transverse (ST) correlations. We find that HD correlations are the best fit to the data and no significant evidence in favor of ST correlations. While Bayes factors show strong evidence for a correlated signal, the data does not strongly prefer either correlation signature, with Bayes factors ∼2 when comparing HD to ST correlations, and ∼1 for HD plus ST correlations to HD correlations alone. However, when modeled alongside HD correlations, the amplitude and spectral index posteriors for ST correlations are uninformative, with the HD process accounting for the vast majority of the total signal. Using the optimal statistic, a frequentist technique that focuses on the pulsar-pair cross-correlations, we find median signal-to-noise ratios of 5.0 for HD and 4.6 for ST correlations when fit for separately, and median signal-to-noise ratios of 3.5 for HD and 3.0 for ST correlations when fit for simultaneously. While the signal-to-noise ratios for each of the correlations are comparable, the estimated amplitude and spectral index for HD are a significantly better fit to the total signal, in agreement with our Bayesian analysis. 

Abstract Analyses of pulsar timing data have provided evidence for a stochastic gravitational wave background in the nanohertz frequency band. The most plausible source of this background is the superposition of signals from millions of supermassive black hole binaries. The standard statistical techniques used to search for this background and assess its significance make several simplifying assumptions, namely (i) Gaussianity, (ii) isotropy, and most often, (iii) a power-law spectrum. However, a stochastic background from a finite collection of binaries does not exactly satisfy any of these assumptions. To understand the effect of these assumptions, we test standard analysis techniques on a large collection of realistic simulated data sets. The data-set length, observing schedule, and noise levels were chosen to emulate the NANOGrav 15 yr data set. Simulated signals from millions of binaries drawn from models based on the Illustris cosmological hydrodynamical simulation were added to the data. We find that the standard statistical methods perform remarkably well on these simulated data sets, even though their fundamental assumptions are not strictly met. They are able to achieve a confident detection of the background. However, even for a fixed set of astrophysical parameters, different realizations of the universe result in a large variance in the significance and recovered parameters of the background. We also find that the presence of loud individual binaries can bias the spectral recovery of the background if we do not account for them. 

Abstract The North American Nanohertz Observatory for Gravitational Waves (NANOGrav) has reported evidence for the presence of an isotropic nanohertz gravitational-wave background (GWB) in its 15 yr data set. However, if the GWB is produced by a population of inspiraling supermassive black hole binary (SMBHB) systems, then the background is predicted to be anisotropic, depending on the distribution of these systems in the local Universe and the statistical properties of the SMBHB population. In this work, we search for anisotropy in the GWB using multiple methods and bases to describe the distribution of the GWB power on the sky. We do not find significant evidence of anisotropy. By modeling the angular power distribution as a sum over spherical harmonics (where the coefficients are not bound to always generate positive power everywhere), we find that the Bayesian 95% upper limit on the level of dipole anisotropy is (C_l=1/C_l=0) < 27%. This is similar to the upper limit derived under the constraint of positive power everywhere, indicating that the dipole may be close to the data-informed regime. By contrast, the constraints on anisotropy at higher spherical-harmonic multipoles are strongly prior dominated. We also derive conservative estimates on the anisotropy expected from a random distribution of SMBHB systems using astrophysical simulations conditioned on the isotropic GWB inferred in the 15 yr data set and show that this data set has sufficient sensitivity to probe a large fraction of the predicted level of anisotropy. We end by highlighting the opportunities and challenges in searching for anisotropy in pulsar timing array data.